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.................................................................Wave–particle dualityof C60 moleculesMarkus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller,Gerbrand van der Zouw & Anton Zeilinger

Institut fur Experimentalphysik, Universitat Wien, Boltzmanngasse 5,A-1090 Wien, Austria

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Quantum superposition lies at the heart of quantum mechanicsand gives rise to many of its paradoxes. Superposition of deBroglie matter waves1 has been observed for massive particlessuch as electrons2, atoms and dimers3, small van der Waalsclusters4, and neutrons5. But matter wave interferometry withlarger objects has remained experimentally challenging, despitethe development of powerful atom interferometric techniques forexperiments in fundamental quantum mechanics, metrology andlithography6. Here we report the observation of de Broglie waveinterference of C60 molecules by diffraction at a material absorp-tion grating. This molecule is the most massive and complexobject in which wave behaviour has been observed. Of particularinterest is the fact that C60 is almost a classical body, because of itsmany excited internal degrees of freedom and their possiblecouplings to the environment. Such couplings are essential forthe appearance of decoherence7,8, suggesting that interferenceexperiments with large molecules should facilitate detailedstudies of this process.

When considering de Broglie wave phenomena of larger andmore complex objects than atoms, fullerenes come to mind assuitable candidates. After their discovery9 and the subsequentinvention of efficient mass-production methods10, they becameeasily available. In our experiment (see Fig. 1) we use commercial,99.5% pure, C60 fullerenes (Dynamic Enterprises Ltd, Twyford, UK)which were sublimated in an oven at temperatures between 900 and1,000 K. The emerging molecular beam passed through twocollimation slits, each about 10 mm wide, separated by a distanceof 1.04 m. Then it traversed a free-standing nanofabricated SiNx

grating11 consisting of nominally 50-nm-wide slits with a 100-nmperiod.

At a further distance of 1.25 m behind the diffraction grating, theinterference pattern was observed using a spatially resolving detec-tor. It consisted of a beam from a visible argon-ion laser (24 W alllines), focused to a gaussian waist of 8 mm width (this is the sizerequired for the light intensity to drop to 1/e2 of that in the centre ofthe beam). The light beam was directed vertically, parallel both tothe lines of the diffraction grating and to the collimation slits. Byusing a suitable mirror assembly, the focus could be scanned withmicrometre resolution across the interference pattern. Theabsorbed light then ionized the C60 fullerenes via heating andsubsequent thermal emission of electrons12. The detection region

was found to be smaller than 1 mm in height, consistent with a fullRayleigh length of 800 mm and the strong power dependence of thisionization process. A significant advantage of the thermionicmechanism is that it does not detect any of the residual gasespresent in the vacuum chamber. We could thus achieve dark countrates of less than one per second even under moderately highvacuum conditions (5 3 10 2 7 mbar). The fullerene ions werethen focused by an optimized ion lens system, and accelerated toa BeCu conversion electrode at −9 kV where they induced theemission of electrons which were subsequently amplified by aChanneltron detector.

Alignment is a crucial part of this experiment. In order to be ableto find the beam in the first place, our collimation apertures aremovable piezo slits that can be opened from 0 to 60 mm (in the caseof the first slit) and from 0 to 200 mm (for the second slit). Thevacuum chamber is rigidly mounted on an optical table togetherwith the ionizing laser, in order to minimize spatial drifts.

The effect of gravity also had to be considered in our set-up. Forthe most probable velocity (220 m s−1), the fullerenes fall by 0.7 mmwhile traversing the apparatus. This imposes a constraint on themaximum tilt that the grating may have with respect to gravity. As atypical diffraction angle into the first-order maximum is 25 mrad,one can tolerate a tilt angle of (at most) about one mrad beforemolecules start falling from one diffraction order into the trajectoryof a neighbouring order of a different velocity class. Theexperimental curves start to become asymmetric as soon as thegrating tilt deviates by more than 500 mrad from its optimumvertical orientation.

The interference pattern of Fig. 2a clearly exhibits the centralmaximum and the first-order diffraction peaks. The minimabetween zeroth and first orders are well developed, and are due todestructive interference of C60 de Broglie waves passing throughneighbouring slits of the grating. For comparison, we show in Fig. 2bthe profile of the undiffracted collimated beam. The velocitydistribution has been measured independently by a time-of-flightmethod; it can be well fitted by f ðvÞ ¼ v3expð 2 ðv 2 v0Þ

2=v2mÞ, with

v0 ¼ 166 m s 2 1 and vm ¼ 92 m s 2 1 as expected for a transitionbetween a maxwellian effusive beam and a supersonic beam13. Themost probable velocity was v ¼ 220 m s 2 1, corresponding to a deBroglie wavelength of 2.5 pm. The full-width at half-maximum wasas broad as 60%, resulting in a longitudinal coherence length ofabout 5 pm.

The essential features of the interference pattern can be under-stood using standard Kirchhoff diffraction theory14 for a gratingwith a period of 100 nm, by taking into account both the finitewidth of the collimation and the experimentally determined veloc-ity distribution. The parameters in the fit were the width of thecollimation, the gap width s0 of a single slit opening, the effectivebeam width of the detection laser and an overall scaling factor. Thismodel, assuming all grating slits to be perfect and identical,reproduces very well the central peak of the interference patternshown in Fig. 2a, but does not fit the ‘wings’ of this pattern.

Agreement with the experimental data, including the ‘wings’ in

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Oven

Collimation slits

100 nm diffractiongrating

Iondetectionunit

10 mµ 10 mµ

Laser

Scanning photo-ionization stage

Figure 1 Diagram of the experimental set-up (not to scale). Hot, neutral C60 moleculesleave the oven through a nozzle of 0:33 mm 3 1:3 mm 3 0:25 mm(width 3 height 3 depth), pass through two collimating slits of 0:01 mm 3 5 mm(width 3 height) separated by 1.04 m, traverse a SiNx grating (period 100 nm) 0.1 m afterthe second slit, and are detected via thermal ionization by a laser 1.25 m behind thegrating. The ions are then accelerated and directed towards a conversion electrode. Theejected electrons are subsequently counted by a Channeltron electron multiplier. Thelaser focus can be reproducibly scanned transversely to the beam with 1-mm resolution.

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Fig. 2a, can be achieved by allowing for a gaussian variation of theslit widths over the grating, with a mean open gap width centred ats0 ¼ 38 nm with a full-width at half-maximum of 18 nm. That best-fit value for the most probable open gap width s0 is significantlysmaller than the 55 6 5 nm specified by the manufacturer (T. A.Savas and H. Smith, personal communication). This trend isconsistent with results obtained in the diffraction of noble gasesand He clusters, where the apparently narrower slit was interpretedas being due to the influence of the van der Waals interaction withthe SiNx grating during the passage of the molecules15. This effect isexpected to be even more pronounced for C60 molecules owing totheir larger polarizability. The width of the distribution seems alsojustified in the light of previous experiments with similar gratings:both the manufacturing process and adsorbents could accountfor this fact (ref. 16, and T. A. Savras and H. Smith, personalcommunication). Recently, we also observed interference of C70

molecules.Observation of quantum interference with fullerenes is interest-

ing for various reasons. First, the agreement between our measuredand calculated interference contrast suggests that not only thehighly symmetric, isotopically pure 12C60 molecules contribute tothe interference pattern but also the less symmetric isotopomericvariants 12C59

13C and 12C5813C2 which occur with a total natural

abundance of about 50%. If only the isotopically pure 12C60

molecules contributed to the interference, we would observe amuch larger background.

Second, we emphasize that for calculating the de Broglie wave-length, l ¼ h=Mv, we have to use the complete mass M of the object.Thus, each C60 molecule acts as a whole undivided particle during itscentre-of-mass propagation.

Last, the rather high temperature of the C60 molecules impliesbroad distributions, both of their kinetic energy and of their internalenergies. Our good quantitative agreement between experiment andtheory indicates that the latter do not influence the observedcoherence. All these observations support the view that each C60

molecule interferes with itself only.

In quantum interference experiments, coherent superpositiononly arises if no information whatsoever can be obtained, even inprinciple, about which path the interfering particle took. Interac-tion with the environment could therefore lead to decoherence. Wenow analyse why decoherence has not occurred in our experimentand how modifications of our experiment could allow studies ofdecoherence using the rich internal structure of fullerenes.

In an experiment of the kind reported here, ‘which-path’ infor-mation could be given by the molecules in scattering or emissionprocesses, resulting in entanglement with the environment and aloss of interference. Among all possible processes, the following arethe most relevant: decay of vibrational excitations via emission ofinfrared radiation, emission or absorption of thermal blackbodyradiation over a continuous spectrum, Rayleigh scattering, andcollisions.

When considering these effects, one should keep in mind thatonly those scattering processes which allow us to determine the pathof a C60 molecule will completely destroy in a single event theinterference between paths through neighbouring slits. Thisrequires l p d; that is, the wavelength l of the incident or emittedradiation has to be smaller than the distance d between neighbour-ing slits, which amounts to 100 nm in our experiment. When thiscondition is not fulfilled decoherence is however also possible viamulti-photon scattering7,8,17.

At T < 900 K, as in our experiment, each C60 molecule has onaverage a total vibrational energy of Ev < 7 eV (ref. 18) stored in 174vibrational modes, four of which may emit infrared radiation atlvib < 7–19 mm (ref. 10) each with an Einstein coefficient ofAk < 100 s 2 1 (ref. 18). During its time of flight from the gratingtowards the detector (t < 6 ms) a C60 molecule may thus emit onaverage 2–3 such photons.

In addition, hot C60 has been observed19 to emit continuousblackbody radiation, in agreement with Planck’s law, with a mea-sured integrated emissivity of e < 4:5 ð 6 2:0Þ 3 10 2 5 (ref. 18). Fora typical value of T < 900 K, the average energy emitted during thetime of flight can then be estimated as only Ebb < 0:1 eV. Thiscorresponds to the emission of (for example) a single photon atl < 10 mm. Absorption of blackbody radiation has an even smallerinfluence as the environment is at a lower temperature than themolecule. Finally, since the mean free path for neutral C60 exceeds100 m in our experiment, collisions with background molecules canbe neglected.

As shown above, the wavelengths involved are too large for singlephoton decoherence. Also, the scattering rates are far too small toinduce sufficient phase diffusion. This explains the decoupling ofinternal and external degrees of freedom, and the persistence ofinterference in our present experiment.

A variety of unusual decoherence experiments would be possiblein a future extension of the experiment, using a large-area inter-ferometer. A three-grating Mach–Zehnder interferometer6 seems tobe a particularly favourable choice, since for a grating separation ofup to 1 m we will have a molecular beam separation of up to 30 mm,much larger than the wavelength of a typical thermal photon. In thiscase, the environment obtains ‘which-path’ information eventhrough a single thermal photon, and the interference contrastshould thus be completely destroyed. The parameters that could becontrolled continuously in such an experiment would then be theinternal temperature of the fullerenes, the temperature of theenvironment, the intensity and frequency of external laser radiation,the interferometer size, and the background pressure of variousgases.

An improved interferometer could have other applications. Forexample, in contrast to previous atom-optical experiments20–22

which were limited to the interaction with only a few lines in thewhole spectrum, interferometry with fullerenes would enable us tostudy these naturally occurring and ubiquitous thermal processesand wavelength-dependent decoherence mechanisms for (we

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b

a

–100 –50 0 50 1000

50

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nts

in 1

sC

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Figure 2 Interference pattern produced by C60 molecules. a, Experimental recording(open circles) and fit using Kirchhoff diffraction theory (continuous line). The expectedzeroth and first-order maxima can be clearly seen. Details of the theory are discussed inthe text. b, The molecular beam profile without the grating in the path of the molecules.

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believe) the first time. Another possible application of moleculeinterferometry is precision metrology; the improved interferometercould be used to measure molecular polarizabilities6. Moreover, itmight be possible to nanofabricate SiC patterns on Si substratesusing C60 interferometry.

Furthermore, we note the fundamental difference between iso-topically pure C60, which should exhibit bosonic statistics, and theisotopomers containing one 13C nucleus, which should exhibitfermionic statistics. We intend to explore the possibility of obser-ving this feature, for example by showing the different rotationalsymmetry between the two species in an interferometer23,24.

In our experiment, the de Broglie wavelength of the interferingfullerenes is already smaller than their diameter by a factor of almost400. It would certainly be interesting to investigate the interferenceof objects the size of which is equal to or even bigger than thediffracting structure. Methods analogous to those used for thepresent work, probably extended to the use of optical diffractionstructures, could also be applied to study quantum interference ofeven larger macromolecules or clusters, up to small viruses25,26. M

Received 30 June; accepted 2 September 1999.

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16. Grisenti, R. E. et al. He atom diffraction from nanostructure transmission gratings: the role of

imperfections. Phys. Rev. A (submitted).

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superhot C60 molecules. Phys. Rev. Lett. 74, 510–513 (1995).

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AcknowledgementsWe thank M. Haluska, H. Kuzmany, R. Penrose, P. Scheier, J. Schmiedmayer and G. Sennfor discussions. This work was supported by the Austrian Science Foundation FWF, theAustrian Academy of Sciences, the TMR programme of the European Union, and the USNSF.

Correspondence and requests for materials should be addressed to A.Z.(e-mail: zeilinger-office@exp.univie.ac.at).

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.................................................................Lanthanum-substituted bismuthtitanate for use innon-volatile memoriesB. H.Park*, B. S. Kang*, S. D. Bu*, T. W. Noh*, J. Lee† & W. Jo‡

* Department of Physics and Condensed Matter Research Institute,Seoul National University, Seoul 151-742, Korea† Department of Materials Engineering, Sung Kyun Kwan University,Suwon 440-746, Korea‡ LG Corporate Institute of Technology, Seoul 137-140, Korea

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Non-volatile memory devices are so named because they retaininformation when power is interrupted; thus they are importantcomputer components. In this context, there has been consider-able recent interest1,2 in developing non-volatile memories thatuse ferroelectric thin films—‘ferroelectric random access mem-ories’, or FRAMs—in which information is stored in the polariza-tion state of the ferroelectric material. To realize a practicalFRAM, the thin films should satisfy the following criteria: com-patibility with existing dynamic random access memory technol-ogies, large remnant polarization (Pr) and reliable polarization-cycling characteristics. Early work focused on lead zirconatetitanate (PZT) but, when films of this material were grown onmetal electrodes, they generally suffered from a reduction of Pr

(‘fatigue’) with polarity switching. Strontium bismuth tantalate(SBT) and related oxides have been proposed to overcome thefatigue problem3, but such materials have other shortcomings,such as a high deposition temperature. Here we show thatlanthanum-substituted bismuth titanate thin films provide apromising alternative for FRAM applications. The films arefatigue-free on metal electrodes, they can be deposited at tem-peratures of ,650 8C and their values of Pr are larger than those ofthe SBT films.

The structure of FRAM is very similar to that of conventionaldynamic random access memory (DRAM), where memory cells arearranged in a square matrix. (Therefore, FRAM should, in principle,have a lower power requirement, a faster access time and apotentially lower cost than many other non-volatile memorydevices1,3.) A DRAM cell usually has a capacitor, where the binaryinformation will be stored in terms of the signs of the stored charge.To maintain this information, a voltage should be continuallyapplied to compensate for charge reduction due to leakage currents.In FRAM, the dielectric material in the capacitor is replaced with aferroelectric film. Then, information can be stored in the polariza-tion states of the ferroelectric thin film: that is, two spontaneouspolarization states under zero electric field can be utilized as ‘0’ and‘1’ digital states. It seems that the first generation of FRAM will bebased on a destructive reading scheme, where a bit is read when apositive switching voltage (that is, an applied electric field) isapplied to the memory cell2. If the cell polarization is alreadyalong the same direction, then only a linear non-switching response,Pns, is measured. If it is in the opposite direction, a switchingresponse, Psw, is measured. Therefore (Psw 2 Pns), which should benearly the same as 2Pr, is an important quantity which determinesthe performance of FRAM. It should be large enough for signaldetection and should not change under repetitive read/write cycles.

The PZT and other related ferroelectric films, which are mostwidely investigated, usually have large values of (Psw 2 Pns): depend-ing on substituting elements and processing conditions, reportedvalues vary from 20 to 70 mC cm−2 (refs 4, 5). However, when acapacitor is fabricated with the PZT film on conventional platinum(Pt) electrodes, its value of (Psw 2 Pns) is usually reduced afterrepetitive read/write cycles. This fatigue problem might be induced